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I would use an arduino microcomputer with an arduino display shield for the display.
The best microcomputers are about 22$ down to a few dollars for the ones from China.
The arduino display shields are around 10$ or so. The Utlransonic distance measuring transducer senors
are less than 10$; they detect if you are in your seat or not.
https://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias%3Daps&amp;field-keywords=arduino+uno
https://www.amazon.com/s/ref=nb_sb_ss_i_1_13?url=search-alias%3Daps&amp;field-keywords=arduino+ping+sensor&amp;sprefix=arduino+ping+%2Caps%2C215&amp;crid=DDBCCF7NH7CK
https://www.amazon.com/s/?ie=UTF8&amp;keywords=arduino+display+shield&amp;tag=geminipcstand-20&amp;index=aps&amp;hvadid=28314448797&amp;hvqmt=e&amp;hvbmt=e&amp;hvdev=c&amp;ref=pd_sl_83ujuhent2_e

One can go from 50hz ac to 12 vdc via battery charger then from 12 vdc battery to 60hz 120v via a dc to ac converter.
see:
https://www.bing.com/videos/search?q=50hz+to+60hz+converter&&view=detail&mid=3D9219028DABBB0162A53D9219028DABBB0162A5&&FORM=VDRVRV&ajf=60

Hello,
I would think few of us would know anything about mig welders. I gather you want to hot switch the current from the mains
to the welder. What current does your welder draw would be a start. You may need a high current relay to do the switching.
Like? https://www.grainger.com/product/5ZH38?cm_mmc=PPC:+Google+PLA&s_kwcid=AL!2966!3!166591437759!!!g!81032003877!&ef_id=WqqIQwAAAacd4m57:20180315145043:s
It's rated "AC contract rating - relay: 25 amperes at 240 volts ac." You need a relay rated higher than it draws off the mains because of the inductive load - I gather the mig welders have a transformer at the input like an arc welder?

How about 3 terminal adjustable voltage regulators?
see for example: https://www.mouser.com/ProductDetail/ON-Semiconductor-Fairchild/LM317AHVT?qs=%2fha2pyFadugRpOCsw7uJG%2fYkcWjLe5SQfHkipQZSRvGAuHf8Q8Z20lpgQCwyK1vllMxUP7WNhWIGj0RAnAK1dQ%3d%3d
60 volts max and 1.5 amperes. Poke around at Mouser for higher current ones also. There are filters on their site that are helpful.

The power required by the charger would be in the order of: 120 * 0.3 = 36 watts.
The
220/240 To 110/120 Volt European Socket Power Converter Step Down Transformer
off ebay.com are rated 100 watts and not expensive. Order one directly from China; it's just up the big pond from you

I enlarged the image off the Amazon.com but could not read it
https://www.amazon.com/Black-Decker-LCS1620-Lithium-battery/dp/B01M6TQPY2/ref=sr_1_3/141-0275392-4037060?ie=UTF8&qid=1499813460&sr=8-3&keywords=Black+%26+Decker+LCS1620
...but ebay.com has a readable image
http://www.ebay.com/itm/Black-Decker-LCS1620-20v-20-Volt-Lithum-Ion-Battery-Charger-NEW-/272090041874?epid=1640405275&hash=item3f59d48e12:g:mf8AAOSwawpXr3eh
120v @60hz 300ma

This unit will work stand alone (with out a UNO) and has wifi>
https://www.amazon.com/HiLetgo-Version-NodeMCU-Internet-Development/dp/B010O1G1ES/ref=sr_1_22/136-5999016-8336545?ie=UTF8&qid=1496770085&sr=8-22-spons&keywords=arduino+wifi&psc=1
Read the Q/A section.

I gather if you want 1.8 volts out you buy the LP3853ET-1.8/NOPB
and if you want say 2.5 volts you buy the the LP3853ET-2.5/NOPB chip
and so forth. They must define the input voltages for each somewhere?
What do you mean by "Can I use LP3856 here ?" ? What is your application?